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Linear and Semilinear Partial Differential Equations

An Introduction

Radu Precup (Autor)

Buch | Hardcover

XIV, 282 Seiten

2012
De Gruyter (Verlag)
978-3-11-026904-8 (ISBN)

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The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.

Radu Precup, Babeş-Bolyai University of Cluj-Napoca, Romania.

PART I: Classical Theory

1 Preliminaries; 2 Partial differential equations and mathematical modeling; 3 Elliptic boundary value problems; 4 Mixed problems for evolution equations; 5 The Cauchy problem for evolution equations;

PART II: Modern Theory

6 Distributions; 7 Sobolev spaces; 8 Variational theory of elliptic boundary value problems;

PART III: Semi-linear Equations

9 Semi-linear elliptic problems; 10 Semi-linear heat equation; 11 Semi-linear wave equation; 12 Nonlinear Schrodinger equations.

Erscheint lt. Verlag	15.11.2012
Reihe/Serie	De Gruyter Textbook
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	510 g
Themenwelt	Schulbuch / Wörterbuch
	Mathematik / Informatik ► Mathematik ► Analysis
	Sozialwissenschaften ► Pädagogik
Schlagworte	elliptic boundary value problems • elliptic equation • heat equation • partial differential equation • Partial Differential Equation; Elliptic Equation; Heat Equation; Wave Equation; Sobolev Space • Partial differential equations • Partielle Differenzialgleichungen • Sobolev Space • Sobolev spaces • Variational theory • wave equation
ISBN-10	3-11-026904-X / 311026904X
ISBN-13	978-3-11-026904-8 / 9783110269048
Zustand	Neuware